【作者】 姚林泉； 王璠； 黄娟；

【Author】 Lin-quan YAO School of Urban Rail Transportation,Soochow University, 178 Ganjiang East Road,Suzhou,Jiangsu 215021,China Fan WANG School of Science and Technology,Jinan University,601 Huangpu Road,West Guangzhou 510632,China Juan HUANG Computer Application Center,Jiangsu Shagang Group Co.Ltd.,Zhangjiagang,Jiangsu 215600,China

【机构】 江苏省苏州市干将东路178号苏州大学城市轨道交通学院； 广东省广州市黄埔大道西601号暨南大学理工学院； 江苏省张家港市江苏沙钢集团有限公司计算机应用中心；

【摘要】 无网格法是求解微分方程定解问题的一种新数值方法。移动最小二乘近似只要求近似函数在各节点处的误差的平方和最小,对近似函数导数的误差没有任何约束。而广义移动最小二乘近似要求近似函数及其导数在所有节点处的误差的平方和最小的。为了降低计算工作量,本文构造了要求近似函数在全部节点处和任意阶导数在部分节点处误差的平方和最小的改进广义移动最小二乘近似。改进广义移动最小二乘近似不仅对函数值而且对导数值也有很高的精度。该方法很好地应用到平面压电问题中。更多还原

【Abstract】 Meshless method is a new numerical method on problem for determining solution of differential equation.The moving least squares approximation makes only require least squares approximation with regard to functional value at all nodes. It makes no require for the residual of derivative approximation.However,the generalized moving least squares approximation makes require least squares approximation with regard to functional and its derivative value at all nodes. For the sake of decrease the computing time.modifying generalized moving least squares approximation is constructed under adding the residual of high orders derivative only at the portion nodes.The modifying generalized moving least squares approximation has high accuracy not only for function value but also one or higher orders derivative.This method is well applied to plane piezoelectric problem.更多还原